Policy analysis framework for conversational biometrics

ABSTRACT

The present invention describes a framework for the analytical and visual analysis and tuning of complex speaker verification systems guided by a policy finite state machine. The Receiver Operating Curve associated with the acoustic speaker recognition task is transformed into a multi-dimensional Receiver Operating Map (ROM), which results from a probabilistic analysis of the policy state machine. A Detection Cost Function (DCF) Map can be similarly generated. Results indicating that optimization over this surface (or the ROM) is an appropriate way to set thresholds are given.

FIELD OF THE INVENTION

The present invention relates to a system and method for ConversationalBiometrics and more specifically to a policy for guiding ConversationalBiometrics.

BACKGROUND OF THE INVENTION

Conversational Biometrics technology enables a non-intrusive and highlyaccurate mechanism for determining and authenticating speakeridentities, based on the analysis of their voice. ConversationalBiometrics combines acoustic text-independent speaker recognition withadditional verification sources such as spoken knowledge to create themost flexible and robust speaker verification and detection.

Unlike other biometrics, voice contains multiple sources of informationthat can be acquired using existing ubiquitous infrastructure and usedfor recognizing and verifying speaker identities. The primary source isthe speaker's voiceprint, which can be analyzed purely from an acousticperspective, without considering the content being spoken. In additionto the voiceprint, voice also contains information on speaker'sknowledge, and with an integrated conversational interface, the samevoice can be analyzed twice: once for voiceprint match, and again forknowledge match.

Contemporary speaker recognition systems, such as those described in G.N. Ramaswamy, R. D. Zilca, O. Alecksandrovich, “A Programmable PolicyManager For Conversational Biometrics”, EUROSPEECH-2003, Geneve,Switzerland, September, 2003, hereinafter referred to as (“Ramaswamy”)and L. P. Heck, D. Genoud, “Combining Speaker and Speech RecognitionSystems”, ICSLP 2002, Denver, September, 2002, depend on a multiplicityof information sources which provide evidence for the assessment of aspeaker's identity. Conversational Biometrics is one such system (seeRamaswamy); it relies on a speaker's acoustic characteristics as well asthe speaker's anticipated level of knowledge. Chief among the benefitsof this approach are:

-   -   The ability to compensate for corruption of any one source; and    -   Increased confidence in the result due to independent        corroborative information, as described in Ramaswamy and U. V.        Chaudhari, J. Navratil, G. N. Ramaswamy, R. D. Zilca “Future        Speaker Recognition Systems: Challenges and Solutions”, Proc. of        AUTOID-2002, Tarrytown, N.Y., March 2002.        It is also possible that the various sources could provide        contradictory evidence, which on the surface would make the        results inconclusive. However, context may be able to        disambiguate the results.

Thus, to effectively use all of the information available, there mustexist a method for reconciling such contradictory evidence in a policythat guides the analysis of a Conversational Biometrics verificationsystem.

SUMMARY OF THE INVENTION

The present invention presents a method for analyzing an analysisguiding policy within the context of Conversational Biometricsverification architecture. A multi-dimensional Receiver Operating Map(ROM) is generated as a transformation of the acoustic ReceiverOperating Curve (ROC) under the operation of the verification policy.Each dimension of the input vector represents a separate parameter, suchas a threshold, and the output can be either the probability of endingup in the “accept” state or the “reject” state. In addition to theacoustic ROC data, the analysis of the policy requires estimates of theprobability of incorrect answers to the posed questions, which aredependent on whether a target or non-target user is assumed.Optimization over the map can be used to set system parameters, such asthe thresholds.

The present invention discloses a method of visually and analyticallyassessing error rates associated with policy based procedures forverification, such as Conversational Biometrics, of a plurality of knownspeakers, evolution of the procedures being controlled by a statemachine, wherein each of the plurality of known speakers has anassociated acoustic component and a knowledge profile, the methodincluding performing policy based verification using a finite statemachine defined by a set of states, each state having a specified set ofquestions and a plurality of possible state transitions, a statetransition is performed if a transition path condition associated withit is satisfied, the transition path condition includes a plurality ofvariables and a plurality of constants; generating a state transitionpath through the state machine wherein each state transition path isassigned a probability value, these probability values being used forgenerating a Receiver Operating Map; developing a probabilistic analysisof the behavior of the state machine; determining if a transition pathcondition is satisfiable by transforming the plurality of transitionpath conditions into a set of linear constraints on variables; andconstructing a Receiver Operating Map using an acoustic ReceiverOperating Curve and probabilities of knowledge error to map a set ofthresholds, or more generally system parameters, to a false accept rateand a false reject rate, wherein Receiver Operating Map is a function ofa plurality of thresholds/parameters with an output selected from one ofaccept rate and reject rate; tuning thresholds and system parameters byvisually or analytically examining and optimizing over the ReceiverOperating Map.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, aspects, and advantages of the presentinvention will be better understood from the following detaileddescription of preferred embodiments of the invention with reference tothe accompanying drawings that include the following.

FIG. 1 is a state diagram illustrating an example of a policy statemachine;

FIG. 2 is a three dimensional graph illustrating Receiver OperatingCurve Probability of Accept Surfaces (1=−0.5); and

FIG. 3 is a two dimensional graph illustrating Detection Cost Function(based on the Receiver Operating Map) Surface Slice at m=3.0 with 36point interpolation over h.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Preferred embodiments of the present invention will now be described indetail herein below with reference to the annexed drawings. In thedrawings, the same or similar elements are denoted by the same referencenumerals even though they are depicted in different drawings. In thefollowing description, a detailed explanation of known functions andconfigurations incorporated herein has been omitted for conciseness.

Conversational Biometrics (CB) (see Ramaswamy) combines speech andspeaker recognition technologies to validate an identity claim. A CBsession is a turn based directed dialog where claimant's responses toposed questions and auxiliary information constitute a dynamic contextbased on which a decision is made, e.g., “accept”, “reject”, or“continue to another question”. The speech input is analyzed withrespect to a voiceprint match as well as knowledge, or the informationcontent of the speech, match. Accordingly, speaker models have both anacoustic component and a knowledge profile. The knowledge profile can berepresented as a table of questions and speaker specific answers. Ingeneral, however, the profile can contain more information. The acousticmodel is based on the Gaussian Mixture Model-Universal Background Model(GMM-UBM) framework described in G. N. Ramaswamy, J. Navratil, U. V.Chaudhari, R. D. Zilca, “The IBM System For The NIST 2002 CellularSpeaker Verification Evaluation”, ICASSP-2003, Hong Kong, April, 2003,and D. A. Reynolds, T. F. Quatieri, and R. B. Dunn, “SpeakerVerification Using Adapted Gaussian Mixture Speaker Models”, DigitalSignal Processing, Vol. 10, Nos. 1-3, January/April/July 2000. Theacoustic scores are based on the likelihood ratio statistic, whereasknowledge match is taken to be binary.

The dialog in a CB session is guided by a verification policy, which canbe represented as a finite state machine (Policy State Machine). Thefollowing assumptions are made: the Policy State Machine is defined by aset of states, each with a specified set of questions or, moregenerally, topics, and possible transitions to be taken if theassociated condition is satisfied. The transition conditions partitionthe decision variable space, and so only one condition can ever bevalid. The conditions themselves are Boolean expressions withintermediate values determined by expressions with relational and binaryoperators on the decision variables, which can represent quantities suchas the number of correctly answered questions, the acoustic score, etc.Exemplary Policy state machine specifications are considered below usingthe illustration shown in FIG. 1. The states, except for ACCEPT andREJECT which are terminal, have topics which indicate their questionpool and the transitions are labeled with conditions. The particularexample presented in FIG. 1 includes the following states: START,REJECT, ACCEPT, PIN, PERSONAL, and FINANCIAL.

The expressions for the conditions use a number of variables andconstants. There are three acoustic score thresholds: low (l), medium(m), and high (h). The variables are:

-   -   T=Number of topics covered before assessing the transition        conditions,    -   W=Number of topics covered for which the answer given was        incorrect, and    -   S=the current acoustic score (described below in more detail).

Accordingly, the state transition machine illustrated in FIG. 1 can bedescribed as Follows:

In the START state, three transitions may be performed:

-   -   If (W=l)&(S<=l), the machine transitions to the REJECT state;    -   If (W=0)&(S>h), the machine transitions to the ACCEPT state; and    -   If (W=0)&(S<=h)|(W>0)&(S>l), the machine transitions to the PIN        state.

In the PIN state, two transitions may be performed:

-   -   If (T−W>=2)&(S>m), the machine transitions to the ACCEPT state;        and    -   If (T−W<2)&(S>m)|(S<=m), the machine transitions to the PERSONAL        state.

In the PERSONAL state, four transitions may be performed:

-   -   If (S>l)&(S<=m)&(W=0)&(T<6), the machine loops and stays in the        PERSONAL state;    -   If        (T>6)|(S>l)&(S<=m)&(W<3)&(T=6)|(S<=1)&(T<=6)|(S>1)&(W>=3)&(T<=6),        the machine transitions to the REJECT state;    -   If (S>m)&(W>3)&(T<=6), the machine transitions to the ACCEPT        state; and    -   If (S>l)&(S<=m)&(3>W>0)&(T<6), the machine transitions to the        FINANCIAL state.

In the FINANCIAL state, three transitions may be performed:

-   -   If        (T>6)|(S>l)&(S<=m)&(W<3)&(T=6)|(S<=1)&(T<=6)|(S>l)&(W>=3)&(T<=6),        the machine transitions to the REJECT state;    -   If (S>l)&(S<=m)&(W<3)&(T<6), the machine loops and stays in the        FINANCIAL state; and    -   If (S>m)&(W<3)&(T<=6), the machine transitions to the ACCEPT        state.

A CB session generates a path through the state machine, which consistsof the following steps:

-   1. asking a question associated with a state, initially the start    state, that has not been asked before on the path,-   2. obtaining the response and score, and-   3. processing the conditions associated with the state transitions    in a sequential or random manner until one is satisfied;-   4. performing the corresponding transition; and-   5. repeating the process (steps 1 to 4) at the next state, unless it    is a terminal state, whereupon an accept or reject decision is made.

The use of a verification policy implies that the analysis of theoverall system performance is not straightforward, because for examplethe different components may give contradictory evidence. Herein aprobabilistic analysis of the behavior of the policy state machine isdeveloped, which affords a general view of system performance and whichfurthermore facilitates the tuning of parameters.

Let P=set of all possible paths determined by the topographicalstructure of the Policy State Machine. Policy analysis first determinesP_(sat)⊂P=subset of paths which are allowed (satisfiable) by thetransition conditions via a recursive procedure which starts in theinitial state of the policy and follows paths depending on whether ornot the conditions associated with the state transitions can besatisfied. Subsequently, each path is assigned a probability leading tothe generation of the Receiver Operating Map, which will be describedbelow in more detail. Note that the transition conditions in FIG. 1ensure a finite number of paths.

To determine if a path condition is satisfiable, transition conditionsare transformed into a set of linear constraints on variables. Theseconstraints are propagated along the given path. At any point in thepath, the linear constraints can be analyzed to determine whether or nota solution exists. A Linear Program is constructed from the set ofconstraints and solved. The feasible set is analyzed to determine thenature of the solutions possible for the program. If the feasible set isempty, then that sequence of transitions is not possible. If desired,the objective function for the Linear Program can be constructed to findthe volume of scores and variable values that determine that path. Ingeneral, the nature of the variables requires a Mixed Integer (MI)Program.

Variable Transformation

To facilitate the analysis, the variables in the transition conditionsmust be represented as sums of variables up to the current depth, whichis equal to the number of turns completed in the dialog. Thus,T=Σ^(depth) _(i=l) q_(i), where q_(i) is the indicator functionindicating if a question was asked at turn i. W=Σ^(depth) _(i=1)w_(i),where w_(i) is the indicator function indicating if an incorrect answerwas given at turn i. S=Σ^(depth) _(i=l)δ_(i), where δ_(i) is the changein acoustic score for turn i.

Condition Transformation

Then, for example, a condition such as(T=3) & (W=2) & (S<3.4)  (1)at depth=3 (where & AND) is transformed toq₁+q₂+q₃ 3−q₁−q₂−q₃ −3w₁+w₂+w₃ <=2−w₁−w₂−w₃ −2δ₁+δ₂δ₃ 3.41≦q_(i)≦1, w_(i)CE{0,1}, LB≦δ_(i)≦UB,where LB and UB are lower and upper bounds derived from the acoustic ROCdata. A long path will have many such combinations and the associatedlinear (MI) Program will be large.

For a path to be viable, all conditions that are associated with thesequence of transitions needed to generate the path must be satisfied.This determination is made at any point in the path by transforming andpropagating the constraints through the path to that point and solvingthe associated program. As an example, consider two segments of onepossible path through the policy: Condition (1) yields the firsttransition, followed by condition (2) (|≡OR) for the second transition(at depth=4).((T−W≦2) & (S≧4.0))|(S≧5.1)  (2)Combining (1) and (2) gives (OR and AND are used for emphasis):(T=3) & (W=2) & (S≦3.4) AND [((T−W≦2) & (S≧4.0))|(S≧5.1)]which is the same as:(T=3) & (W=2) & (S≦3.4) & (T−W≦2) & (S≧4.0))OR(T=3) & (W=2) & (S<3.4) & (S>5.1)and which corresponds to the following set of ORed programs (bounds asbefore):q₁+q₂+q₃3−q₁−q₂q₃ −3w₁+w₂+w₃ <=2−w₁−w₂−w₃ −2δ₁+δ₂+δ₃ 3.4q₁+q₂+q₃+q₄−w₁−w₂−w₃−w₄ 2−δ₁−δ₂−δ₃−δ₁ 4.0ORq_(i)+q₂+q₃ 3−q₁−q₂−q_(3l)−3w₁+w₂+w₃ <=2−w₁−w₂−w₃ −2δ₁+δ₂+δ₃ 3.4−δ₁−δ₂−δ₃−δ₁ −5.1

One purpose of the ROC curve is to map a threshold to false accept andfalse reject rates. Here a Receiver Operating Map (ROM) is defined as afunction of the multiple thresholds, or in general the parameters in thepolicy. The output can be either the “accept rate”, which is theprobability of ending up in the ACCEPT state or the reject rate=1−acceptrate, which is the probability of ending up in the REJECT state. Theinterpretation of the output of the map, i.e., whether it is the falseaccept rate or the false reject rate, is dependent on whether a targetor non-target (imposter) session is assumed. The ROM surface isgenerated by calculating these values over a grid in a volume ofthreshold (parameter) values. The first step is to associate with eachcondition, a probability (or density where appropriate) of occurrence bytreating each variable in the policy as a random variable with a knownor derived distribution. For example, let p(S) be the distribution ofthe score variable for a target model. It is used, along with thenon-target distribution, in determining the acoustic only ROC curve.This is the distribution used on the first point in the path. At thesecond point, the distribution is conditioned on the transitioncondition that was satisfied to bring the system to the current state(point in the path). Here it is assumed that if the first conditioncontained the statement S>1.1, then the new score distribution isp(S|S>1.1), which is easily derivable from p(S), etc. for subsequentpath points. The distributions depend on the depth along the path andprevious variable observations. Note that the analysis is simplified byexpanding the policy state machine, replacing a transition whosecondition has ORed components with a set of individual transitions foreach component. For the present, assume that the acoustic score, T, andW are conditionally independent given whether the session is target ornon-target. The value of W is based on the (hypothesized) probability ofhaving a given piece of knowledge, i.e., the likelihood that a targetwill know the answer to a particular topic question as well as thelikelihood that a non-target will know the answer. These may bedetermined, for example, via the difficulty of the questions, or byempirical evidence. Since the transition conditions for each statepartition the decision variable space, the sum of the probabilities ofall allowable (satisfiable) paths from the start node to the ACCEPT andREJECT nodes is 1. Given the probability assignments, the ROM can bespecified. Let P_(accept)⊂P_(sat) be the subset of paths that end in theACCEPT state and P_(reject), the subset that end in the REJECT state.Let t⁻ be a threshold vector defined by the grid. Then the specificationof the ROM is the computation, for every t⁻ in the grid, ofProb[P_(accept)|t⁻]=the sum of the probabilities of all paths inP_(accept) given t⁻.

Consider, again, the policy state machine specifications shown inFIG. 1. Define a grid of threshold values (see description of FIG. 2below) in 3 dimensions, one each for the low (l), medium (m), and high(h) score thresholds. For each threshold vector given by the grid, aprobability of accept (1-reject) is computed as outlined above. FIG. 2shows the resulting ROM surfaces (R²→R, or accept rate as a function ofm and h, where 1 is kept constant) for three different classes of usersfor the policy in FIG. 1 (the h axis ranges from 1 to 8 corresponding tounit threshold increments from 0 up to 7, and the m axis runs from 1 to6 corresponding to unit threshold increments from 0 up to 5, the lowthreshold is fixed at −0.5). The upper surface corresponds to targets,who are the correct speakers. The middle surface corresponds to informedimposters, i.e., impersonators who have gained access to the correctknowledge. The lowest surface corresponds to uninformed imposters, whoare impersonators without correct knowledge. Each class of usercorresponds to different probability assignments for the transitionconditions, determined by the input score distribution, which here istaken from real usage of the policy in FIG. 1, and the input probabilityof errors for the questions for both targets and non-targets. The lattercan be estimated from the complexity of the questions, the speechrecognition error rate, etc. In this analysis, they were kept fixed at0.05 for the targets and 0.95 for the non-targets, rates that wereconsistent with empirical results.

FIG. 2 clearly highlights the fact that a poor choice of thresholds willmake the system unusable, even if the components themselves performwell. Thus, a method to properly set the thresholds can be developed.Given that the probabilities of accept and reject can be computed fortargets and imposters, we can compute the values of the Detection CostFunction (DCF), a weighted combination of false accept and false rejectrates, defined for the National Institute of Standards and Technology(NIST) Speaker Recognition Evaluations, described in “The NIST Year 2002Speaker Recognition Evaluation Plan”, NIST, 2002, as a function of thedimensions (thresholds). This generates a corresponding surface to theROMs.

FIG. 3 shows a slice of the DCF surface at m=3.0 for both an informedand uninformed imposter. The slice is interpolated over the h axis on 36equal spaced points from 1 to 7. The values to which the curves convergedepend on the fixed thresholds and could be reduced by their adjustment.Note that as h is reduced, an informed imposter will readily beaccepted. To understand the predictive power of this analysis, alsoshown as circles and squares are the locations of the hand tunedoperating points for real test data generated during use of the policy.Optimization (minimization) along the DCF slices yields performance veryclose to the hand tuned operating points. This remains true for otherslices at different thresholds, suggesting that searching for theminimum point on the full DCF surface is a good way to automatically setthe multiple thresholds. This range of thresholds is also indicated inFIG. 2 by the contrasting rectangles.

The present invention, therefore, presents a method to analytically andgraphically assess the error rates associated with policy basedverification procedures whose evolution is controlled by a state machinewith transitions conditioned on the context of the process. The ROM wasdeveloped as a graphical means to view system performance and replacesthe ROC for these complex verification systems. Analysis based tuning ofthreshold parameters is also presented, as well as evidence to show thatit agrees with actual performance data. The tuning may be performed byvisually or analytically examining and optimizing over the ROM. Otherapplications, such as policy based dialog management systems may alsobenefit from the presented analysis methods.

While the invention has been shown and described with reference tocertain preferred embodiments thereof, it will be understood by thoseskilled in the art that various changes in form and details may be madetherein without departing from the spirit and scope of the invention asdefined by the appended claims.

1. A method of assessing error rates and tuning parameters associatedwith policy based procedures for verification of a plurality of knownspeakers through the use of conversational biometrics, evolution of thepolicy based procedures being controlled by a state machine and each ofthe plurality of known speakers has an associated acoustic component anda knowledge profile, the method comprising the steps of: performing apolicy based verification using a finite state machine defined by a setof states, each state having a specified set of questions and aplurality of possible state transitions, a state transition beingperformed if a condition of a state transition path associated with thestate transition is satisfied; determining allowability of thecondition; generating a state transition path through the state machine;identifying all allowable state transition paths; developing aprobabilistic analysis of the behavior of the state machine, whereineach allowable state transition path is assigned a probability value;generating a Receiver Operating Map (ROM) by using said probabilityvalues; mapping a set of thresholds/parameters to a false accept rateand a false reject rate by using an acoustic Receiver Operating Curveand probabilities of knowledge error, wherein the ROM is a function of aplurality of the thresholds/parameters with an output selected from oneof accept rate and reject rate; and tuning said thresholds/parameters byvisually or analytically examining and optimizing over the ROM.
 2. Themethod of claim 1, wherein allowability of the condition is determinedby transforming a plurality of conditions into a set of linearconstraints or variables and determining a feasible set.
 3. The methodof claim 1, wherein the performing step further includes analyzingspeech input of said known speakers with respect to the acousticcomponent and the knowledge profile of the speech input.
 4. The methodof claim 3, wherein the acoustic component is based on a likelihoodratio statistic and the knowledge profile is represented as a table ofquestions and answers that are specific to each of the plurality of saidknown speakers.
 5. The method of claim 1, wherein the condition includesa plurality of variables and a plurality of constants, the plurality ofconstants including three acoustic score thresholds/parameters: low (l),medium (m), and high (h) and the plurality of variables include T, anumber of topics covered before transition path conditions are assessed,W, a number of topics covered for which the answer given was incorrect,and S, a current acoustic score threshold/parameter.
 6. The method ofclaim 1, wherein the step of generating a state transition path furthercomprises the steps of: a) asking a question associated with a state,the question have not been asked before on the state transition path, b)obtaining a response to the asked question and a response scorethreshold/parameter, c) processing the conditions until one condition issatisfied; d) performing the state transition corresponding to thecondition; and e) repeating steps a) to d) if a present state is not aterminal state and otherwise, making a decision of generating an ACCEPTor REJECT state.
 7. The method of claim 6, wherein the step ofgenerating a state transition path is simulated.
 8. The method of claim1, wherein for the step of identifying is determined according towhether a full linear or mixed integer program of the state transitionpath is solvable.
 9. The method of claim 1, wherein the probabilityvalue of the accept rate is a probability of transitioning to an ACCEPTstate and the probability value of the reject rate is a probability oftransitioning to a REJECT state, the probability value of the rejectrate is indicated as 1-accept rate.
 10. The method of claim 9, whereinthe probability of transitioning to an ACCEPT state is the probabilityof all state transition paths leading to the ACCEPT state and theprobability of transitioning to a REJECT state is the probability of allpaths leading to the REJECT state.
 11. The method of claim 10, whereinthe step of generating a ROM further comprises the steps of: defining agrid of threshold/parameter values in a plurality of dimensions, whereinone dimension is allocated to each of low, medium, and high scorethreshold/parameters; computing the probability value of the acceptrate, or probability value of the reject rate for each set ofthreshold/parameter values given by the grid; creating a visualrepresentation of the accept or reject rates as a function of thethreshold/parameter values given by the grid; and creating arepresentation of the accept or reject rates as a function of thethreshold/parameter values given by the grid.
 12. The method of claim11, wherein an upper surface of the ROM corresponds to a correct speakerof the plurality of known speakers, a middle surface corresponds toinformed impersonators who have gained access to knowledge associatedwith the known speaker, and the lowest surface corresponds to uninformedimpersonators who do not have knowledge associated with the knownspeaker.
 13. The method of claim 11, wherein the tuning step furthercomprises the step of determining one or more desirable points in theROM, based on the probabilities of accept rate and reject rate fortarget known speakers and one or more impersonators of known speakers,wherein said determining is performed using visual inspection of theROM.
 14. The method of claim 11, wherein the tuning step furthercomprises the steps of: evaluating regions of the ROM using analyticalmethods; and determining one or more desirable points in the ROM basedon the probabilities of accept rate and reject rate for target knownspeakers one or more impersonators of known speakers, wherein saiddetermining is performed via analytical optimization.
 15. The method ofclaim 14, wherein the analytical optimization maximizes an objectivefunction.
 16. The method of claim 14, wherein the analyticaloptimization minimizes an objective function.
 17. A method of assessingerror rates and tuning parameters associated with policy basedprocedures for verification of a plurality of known speakers through theuse of conversational biometrics, evolution of the policy basedprocedures being controlled by a state machine and each of the pluralityof known speakers has an associated acoustic component and a knowledgeprofile, the method comprising the steps of: performing a policy basedverification using a finite state machine defined by a set of states,each state having a specified set of questions and a plurality ofpossible state transitions, a state transition being performed if acondition of a state transition path associated with the statetransition is satisfied; generating a Receiver Operating Map (ROM) byusing a plurality of probability values; and mapping a set ofthresholds/parameters to a false accept rate and a false reject rate,wherein the ROM is a function of a plurality of thethresholds/parameters with an output selected from one of accept rateand reject rate.
 18. The method of claim 17, further comprising thesteps of: developing a probabilistic analysis of the behavior of thestate machine, wherein each allowable state transition. path is assigneda probability value; determining allowability of the condition;generating a state transition path through the state machine; andidentifying all allowable state transition paths.
 19. The method ofclaim 18, wherein the mapping step is performed by using an acousticReceiver Operating Curve and probabilities of knowledge error.
 20. Themethod of claim 17, further comprising a step of tuning saidthresholds/parameters by examining and optimizing saidthresholds/parameters over the ROM, wherein said examining andoptimizing is performed by a method selected from a visual andanalytical.
 21. The method of claim 17, wherein the condition includes aplurality of variables and a plurality of constants.